Professor Oak is the first NPC (non-person character) you talk to in the game at the start of the game. He will give you a starter once you start the game. His lab has many things, including a picture that shows his favourite Pokemon, Dragonite. You can also find Professor Oak in Saffron City where if you have 300 Pokemon in your Pokedex, Professor Oak will give you a Heatran.
Oak will give you a starter Pokémon at the very beginning when you start at his lab.
He will also be in Mausoleum of Origin's PokéCenter and will give you either a Mewtwonite X or a Mewtwonite Y. These are Mega Stones for Mewtwo, the Genetic Pokemon. You will need at least 550 Pokedex entries to claim your prize.
Your starter Pokémon is free. However, you must have 300 Pokedex entries to obtain a Heatran from him, and 550 to get Mewtwonite X/Y